The Schwartz-Zippel bound [1]} and combinatorial nullstellensatz [2]} are important tools from both theoretical and application perspectives. The Schwartz-Zippel bound provides an estimate on the number of zeros of a polynomial whose coefficients take values in a finite field and has applications in polynomial comparison, primality testing, perfect matching in graphs etc. The combinatorial nullstellensatz determines conditions under which a polynomial contains a non-zero in a given set whose cardinality is larger than the overall degree of the polynomial. We refer to Chapter 7, [3]} for more material. Recently [4]} have used algebraic techniques to obtain Schwartz-Zippel type bounds for intersection of algeraic varieties with Cartesian products of two-dimensional sets.
